Try logging into the website directly, instead. We haven't ever heard of people having issues downloading this game through the Itch App... But we definitely know it works from the website.
Viewing post in Rewind: A Looping History comments
Ok, I know the problem. I've not done the steps to integrate the game into the Itch app's automatic update system (it's not a difficult process or anything; it's just not been high on my priority list). Until I get that sorted out, the app won't find any usable versioning information, so it won't allow you to select any files to download.
You can still download the raw files from the web portal version of Itch, though (https://sprintingcucumber.itch.io/rewind). I'll make a devlog post when I have everything squared away to work properly with the app sometime over the next few days (my work time is limited during the pandemic dark ages, so I can't promise a quick turnaround).